Question 1184081: The average dividend yield of a random sample of 25 JSE-listed companies this year was found
to be 14.5%, with a sample standard deviation of 3.4%. Assume that dividend yields are
normally distributed.
3.1.1 Calculate, with 90% confidence, the actual mean dividend yield of all JSE-listed
companies this year. Interpret the finding.
3.1.2 Calculate, with 95% confidence, the actual mean dividend yield of all JSE-listed
companies this year. Compare the interval with the one calculated in 3.1.1
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! since the standard deviation is taken from the sample, rather than from the population, use the t-score rather than the z-score.
sample size = 25
sample mean = 14.5%
sample standard deviation = 3.4%
standard error = sample standard deviation divided by square root of sample size = 3.4/sqrt(25) = 3.4/5 = .68
critical t-score with 24 degrees of freedom at 90% two-tailed confidence level = plus or minus 1.711.
critical t-score with 24 degrees of freedom at 95% two-tailed confidence level = plus or minus 2.064.
these were taken from the following table:
http://www.math.odu.edu/stat130/t-tables.pdf
they were also verified through use of the ti-84 plus scientific calculator.
with a critical t-score of plus or minus 1.711, the critical raw score is calculated as shown below:
-1.711 = (x - 14.5) / .68
solve for x to get x = -1.711 * .68 + 14.5 = 13.33652%
1.711 = (x - 14.5) / .68
solve for x to get x = 1.711 * .68 + 14.5 = 15.66345%
with a critical t-score of plus or minus 2.064, the critical raw score is calculated as shown below:
-2.064 = (x - 14.5) / .68
solve for x to get x = -2.064 * .68 + 14.5 = 13.09648%
2.064 = (x - 14.5) / .68
solve for x to get x = 2.064 * .68 + 14.5 = 15.90352%
at 90% confidence level, the range is from 13.33652% to 15.66345%
at 95% confidence level, the range is from 13.09648% to 15.90352%
the range is larger at 95% confidence level than at 90% confidence level.
this is to be expected because there needs to be less change of error at 95% confidence level than at 90% confidence level.
at 90% confidence level, 90% of the sample means, each with a sample size of 25, are expected to be within the range specified.
at 95% confidence level, 95% of the sample means, each with a sample size of 25, are expected to be within the range specified.
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